1. Field of the Invention
The present invention relates to the field of ultrasonics, and more particularly to a method and apparatus for evaluating the physical properties of a sample. The invention can, for example, be used for measuring the diffusion coefficient of ultrasound in a substance, for measuring the absorption coefficient of ultrasound in a substance and for evaluating grain size in a polycrystalline material.
2. Description of Prior Art
Ultrasonic measurement techniques generally involve generating an ultrasonic pulse in an object, and then detecting the signal after propagation in the object to determine its geometrical, microstructural, and physical properties. This technique is advantageous because it is nondestructive and because it can probe the interior of materials. Conventional ultrasonic devices have been developed which involve the use of transducers, including piezoelectric and electromagnetic acoustic transducers (EMATs). Another ultrasonic technique is laser-ultrasonics, wherein one laser with a short pulse is used for generation and another laser coupled to an optical interferometer is used for detection. The detection laser is either a long pulse or continuous laser. Either laser may be coupled to the material under test through an optical fiber for ease of handling.
This approach is advantageous because it does not require either the generation laser or the laser-interferometer detector to be in contact or close to the object. Furthermore, unlike an EMAT or piezoelectric transducer, the generation laser and laser-interferometer are not subject to precise orientation requirements. Details about laser-ultrasonics can be found in C. B. Scruby, L. E. Drain, xe2x80x9cLaser-ultrasonics: techniques and applicationsxe2x80x9d, Adam Hilger, Bristol, UK 1990 and J.-P. Monchalin, xe2x80x9cOptical detection of ultrasound,xe2x80x9d IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 33, 485 (1986).
The absorption coefficient of ultrasound is one parameter that characterizes the physical properties and the interaction of ultrasound with the microstructure of the material. The variation of the absorption coefficient with temperature and ultrasound frequency can provide information about internal friction, relaxation phenomena, magnetic properties of the material, dislocation density, phase transformations, or specific microstructural structures. The simplest approach to the measurement of the absorption is to observe the free decay in the amplitude of a vibration mode of a sample. Another popular approach is to use a forced vibration where one measures the phase difference between the driving system and the vibration of the sample. Both approaches are limited to samples with specific geometries and each measurement only gives the absorption coefficient at one frequency and one temperature. Performing a full study of absorption as a function of frequency and temperature can be quite time consuming.
Ultrasound absorption can also be estimated from the attenuation of propagating waves. A serious limitation to this approach is the difficulty of separating the attenuation due to absorption mechanisms from that due to other phenomena like diffraction, scattering by grains, or scattering by rough surfaces. In 1987, Willems proposed a reverberation technique in which an ultrasonic pulse is first generated at the surface of a sample, then propagates in the material and, due to the finite size of the sample, fully insonifies the latter with incoherent ultrasound after some time. [H. Willems, xe2x80x9cA New Method for the Measurement of Ultrasonic Absorption in Polycrystalline Materialsxe2x80x9d, in D. O. Thompson, D. E. Chimenti (Eds.), Review of the Progress in Quantitative Nondestructive Evaluation, Vol. 6A, p.473, 1987] The measured decrease of the ultrasound amplitude with time can then be solely attributed to absorption mechanisms. When a short laser pulse is used to generate ultrasound, a very wide range of ultrasonic frequencies can be observed. A single measurement then allows the determination of the ultrasound absorption coefficient at many frequencies at once. The main limitation of this technique is that it is restricted to samples with finite volume, making it inappropriate for online measurement.
In 1985, Guo et al. demonstrated experimentally, using conventional transducers and samples of large dimensions, that when an ultrasonic pulse propagates and is scattered by the various structures in a material, it gives rise to an energy cloud of incoherent vibration, termed xe2x80x9cdiffuse ultrasoundxe2x80x9d, and that this energy cloud spreads as governed by the diffusion equation. [C. B. Guo, D. Holler, and K. Goebbels, xe2x80x9cScattering of Ultrasonic Waves in Anisotropic Polycrystalline Metalsxe2x80x9d, Acustica, vol. 59, p. 112, 1985] The vibration energy not only diffuses but is also absorbed in the material by various mechanisms. By observing the time evolution of the diffuse ultrasound, one can evaluate the diffusion and absorption coefficients of ultrasound. This technique has many advantages over the previous ones. Firstly, it can be applied to large samples. Secondly, it provides the absorption and diffusion coefficients of ultrasound, both parameters being useful for the characterization of the microstructure.
However, because the technique utilizes piezo-electric transducers, it is subject to several limitations. One such limitation is that the piezoelectric transducer must be either in direct contact with the object to be measured, or coupled to that object using some type of bonding material. In addition, delay lines, also called buffer rods, are often used to transport the ultrasound from the object to the transducer. Thus, the ultrasound field to be measured leaks out of the object and into the bond and the transducer where it may be attenuated both by the transducer""s, bond""s, or delay line""s material properties and by the conversion of acoustic energy into electrical energy by the transducer. In practice, this limits the application of the technique to objects which show either a high diffusivity or a high absorption so that the decrease in the sound field energy caused by the sample itself is much larger than the decrease in the sound field energy caused by the transducer and its bond or delay line.
Another limitation of the technique is that the piezoelectric transducer has a relatively narrow bandwidth (or order xc2x110% to xc2x150% of the transducer""s center frequency). Wideband transduction is usually preferred because a wideband signal can be made narrowband by filtering, whereas a narrowband signal cannot be made wideband.
Yet another limitation of the technique is that the piezoelectric transducer is of relatively large dimensions. Typical dimensions of such transducers may vary from a few mm in diameter to perhaps 25 mm in diameter. Therefore, these transducers cannot spatially resolve the ultrasound field to an accuracy better than about 1 mm in the best cases. This may cause difficulties when measuring the sound field of a small object, or when attempting to measure the spatial dependence of the sound field as a function of position.
In 1990, Weaver proposed an application of the diffusion coefficient of ultrasound to the characterization of the microstructure of materials. [R. L. Weaver, xe2x80x9cUltrasonic Diffuse Field Measurements of Grain Sizexe2x80x9d, Non-Destructive Testing and Evaluation in Manufacturing and Construction, 1990, p. 425] Theoretical considerations show that the diffusion coefficient behaves like the inverse of the ultrasonic attenuation coefficient due to scattering. This coefficient is related to the grain size of polycrystalline materials. Weaver showed experimentally that the diffusion coefficient of ultrasound is affected by thermal treatment for an AISI 1045 steel, which supports the idea that the technique can be used for the non-destructive measurement of grain size. However, he did not specify a method for obtaining precise grain size measurements estimates from the measured diffusion coefficient. Instead, he plots the material""s measured diffusivity as a function of frequency and observes that those samples which are expected to have larger grain sizes have higher diffusivity. Therefore, one method of estimating grain size from diffusivity is to build a calibration curve of diffusivity as a function of grain size for a specific material at a specific frequency.
However, the applicants have found that one does not have complete freedom in choosing the frequency, and that different samples may be best measured at different frequencies. For example, if the frequency is too low, too little grain scattering may occur and the sample reaches equipartition of energy only when the ultrasound field has spread so much that its amplitude is too small to be measured accurately. Conversely, if the frequency is too high, the absorption coefficient, which usually increases with frequency, may be so high that the ultrasound energy is largely absorbed before equipartition of energy is attained. Again, this may result in ultrasound amplitudes that are too low to be measured accurately.
Therefore it is an object of the present invention to overcome the afore-mentioned limitations of the prior art.
According to the present invention there is provided a method of evaluating the physical properties of a sample, comprising generating an ultrasound field in a local region of the sample with a time-varying source of radiation such that the generated ultrasound diffuses away from said local region; waiting until the generated ultrasound field has reached a diffusion regime; detecting the resulting ultrasound field with a non-contact detector; and adjusting parameters in a mathematical model describing the predicted behaviour of the ultrasound field in the diffusion regime to fit the detected ultrasound field to the mathematical model and thereby derive at least one parameter dependent on the physical properties of the sample.
The invention provides a method of measuring the diffuse acoustic field and its time and spatial dependence using a non-contact, preferably wideband, point-like ultrasound detector, and using a preferably wideband, non-contact, ultrasound generator. In a preferred embodiment, advantage is taken of the wideband characteristics of the ultrasound generator and detector by using time-frequency analysis technique to analyze the time and frequency dependence of the measured signal. However, other techniques may be used, such as analog filtering and processing of the data, or a combination of analog and digital processing.
Advantageously, an ultrasound detector with point-like characteristics can be used to take measurements at one or several precisely measured locations on the sample surface.
The mathematical model is typically a diffusion equation with the initial and boundary conditions appropriate to the sample to be measured. The solution to this equation is numerically fitted to the measured ultrasonic signal so as to obtain the ultrasonic diffusion and absorption coefficients of the object being measured.
For a wideband source of ultrasound, such as a pulsed source of radiation, the physical mechanism which transforms the pulsed radiation into ultrasound does not generate all acoustic modes with equal efficiency. However, the diffusion equation accurately describes the ultrasound field only when the ultrasound has locally populated all ultrasonic modes with substantially equal probability. When this arises, the system is said to have attained a local state of equipartition of energy. By xe2x80x9clocalxe2x80x9d it is understood that although the system has not reached a complete state of equilibrium (the ultrasound field is evolving in time), on short time and lengths scales it appears to be in equilibrium. It is in this case that the diffusion equation is valid and the system is said to be in the diffusion regime. Therefore, one must wait some time, typically anywhere from 1 to 100 xcexcs, for the ultrasound field to attain this state of equipartition. Consequently, the initial conditions to the diffusion-model equation are not those that prevail at the instant of ultrasound generation, but must be taken some time after the instant of ultrasound generation. These initial conditions may rely on an initial-conditions-model describing the ultrasound field some time after the instant of ultrasound generation. Another possibility is to obtain the initial-conditions by measuring the ultrasound field some time after the instant of ultrasound generation. Yet another possibility is to use a combination of a model and measurements. For example, the model may assume one-dimensional behaviour and, because of this assumption, the number of measurements of the ultrasound field required to provide an accurate description of the initial conditions may be greatly reduced. Preferably, all known information or reasonable assumptions regarding the initial conditions are utilized to reduce the number of measurements required.
In 1987, Willems [H. Willems, xe2x80x9cA New Method for the Measurement of Ultrasonic Absorption in Polycrystalline Materialsxe2x80x9d, in D. O. Thompson, D. E. Chimenti (Eds.), Review of the Progress in Quantitative Nondestructive Evaluation, Vol. 6A, p.473, 1987] showed how the absorption coefficient measured using the reverberant technique may be used to estimate the amount of plastic strain present in a cold rolled sample. The absorption coefficient measured using the present invention can also do the same.
In another aspect the invention also provides an apparatus for evaluating the physical properties of a sample, comprising a time-varying source of radiation for generating an ultrasound field in a local region of the sample such that the generated ultrasound diffuses away from said local region; a non-contact detector for detecting the resulting ultrasound field with a delay such that the generated ultrasound field has reached a diffusion regime; and an analyzer for adjusting parameters in a mathematical model describing the predicted behaviour of the ultrasound field in the diffusion regime to fit the detected ultrasound field and thereby derive at least one parameter dependent on the physical properties of the sample. This parameter may be used to infer other derived quantities. For example, the absorption coefficient may be used to infer the amount of plastic deformation in a metal or the yield strength of a metal, and the diffusion coefficient may be used to infer the grain size of a polycrystalline aggregate.
Having written a general description of the invention, we now describe specific aspects in more detail.
Preferably, the ultrasound generator is a pulsed source of radiation because this ultrasound generator can be wideband and allows for various source geometries, although narrowband electromagnetic acoustic transducers (EMAT) could be used as well in some special cases. Preferably the pulsed source of radiation is a pulsed laser, although a flash lamp, a pulsed source of x-rays, a pulsed electron gun, a pulsed source of ions, or a pulse of atomic particles, or any other ultrasound-generating source of radiation could be used.
In a preferred embodiment, a non-contact, point-like, ultrasound detector is used to detect the ultrasound.
In the preferred embodiment, the ultrasound detector is a laser interferometer, although any ultrasound detector based on so-called white-light interferometry or on non-interferometric optical (including infrared and UV wavelengths that behave much like optical wavelengths) technique such as knife edge, surface grating, or reflectivity techniques may be used. (Jean-Pierre Monchalin.  less than  less than Optical detection of ultrsound greater than  greater than  IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. UFFC-33, No. 5, September 1986. p. 485-499.) However, the output of the ultrasound detector should either be linear with ultrasound amplitude (or energy), or could be made linear by the application of a suitable calibration.
Preferably, the interferometer""s output signal is wideband so as to measure as much as possible of the full bandwidth of the generated ultrasonic signal. Preferably, the ultrasound detector will sense a point-like location on the surface of the sample. Point-like in this context means that the dimensions of the location that is being sensed are small compared to the shortest acoustic wavelength being measured. This is desirable, but not absolutely necessary, because if the sensing location is larger, the sample motion caused by the ultrasound will be averaged out and sensitivity will be decreased.
Point-like also means that the dimensions of the location that is being sensed are sufficiently small to provide an accurate measurement of the position of that location. Also, although the detection location is usually on the surface of an object, the detection location may also be inside a transparent object. For example, one can imagine a small reflective particle, or a metallic interface being located inside a piece of glass. This small reflective particle or metallic interface would then reflect the laser light that would be used by the laser interferometer to sense the acoustic amplitude at that location.
Preferably, the processor is composed of a digitizer and a computer. The digitizer converts the analog output of interferometer into a digital signal suitable for further analysis and calculations. The computer provides means to store the digital information at least temporarily while the analysis is being performed, and provides a means to apply various algorithms to best extract the diffusion and absorption coefficients, as well as other derived physical quantities. However, the processor may also be analog (as opposed to digital), although these processors provide less flexibility, and sometimes only provide for the approximate implementation of the analysis algorithms. The computer also stores the diffusion equation and calculates the ultrasound diffusion and absorption coefficients.
Preferably, a range of ultrasonic frequencies is selected such that these frequencies are high enough to cause enough scattering so that the equipartition of energy is locally attained before the ultrasound has diffused away from the detection location, and low enough so that the equipartition of energy is locally attained and the diffuse signal reaches the detection location before the ultrasound is absorbed.
Preferably, a numerical time-frequency analysis technique is used to analyze the time and frequency dependence of the measured signal. Preferably, a short time Fourier transform technique with a low leakage window can be used.
The mathematical model employed may be based on the diffusion equation solved with the initial and boundary conditions appropriate to the object to be measured. The solution is numerically fitted to the measured ultrasonic signal so as to obtain the ultrasonic diffusion and absorption coefficients of the object being measured. In this method, the initial conditions are taken as a model distribution of the acoustic field some time after the instant of ultrasound generation, when the ultrasound field has attained a local equipartition of energy. The initial conditions can also be determined by measuring the energy distribution of the ultrasonic field at any time in the diffusive regime.
It is also understood that a material may not have a single diffusion coefficient. For example, an anisotropic material having orthotropic symmetry may have three coefficients, one for each of the three spatial dimensions. This particular example and the more general case can be taken into account in a multi-dimensional diffusion model and initial conditions, and by a suitable set of measurements.
The fitted diffusion coefficient can be related to the grain size of a polycrystalline aggregate. Dimensional analysis states that xe2x80x9cIf an algebraic equation expresses a relation among physical quantities, it can have meaning only if the terms involved are alike dimensionallyxe2x80x9d. This quote and a formal procedure to apply dimensional analysis can be found in the following reference: Arnold M. Kuethe and Chuen-yen Chow; xe2x80x9cFoundation of Aerodynamics, Bases of Aerodynamic Designxe2x80x9d 4th edition; John Wiley and Sons, New York, 1986; Appendix A: xe2x80x9cDimensional Analysisxe2x80x9d p. 444-448. Although such a formal analysis was made, what follows is an informal description which perhaps better captures the idea behind the proposed method.
For the diffusive propagation of ultrasound, one may choose as a basic set of variables with fundamentally different dimensions, the variables: k=2xcfx80/xcex where xcex is the acoustic wavelength, also called the wave number (units of 1/length); c, the sound velocity (units of length/time); and xcfx81, the materials"" mass density (units of mass/length3). Other basic sets are also possible, but insofar as these other variables can be constructed from the above variables (for example, k can be replaced by the frequency, f, as long as k=2xcfx80f/c), the argument below can be made without loss of generality.
Given that D, the diffusivity, is expressed in units of length2/time, a dimensionless combination of D with the above basic set of variables is Dk/c. In a polycrystalline aggregate, one may model the propagation of ultrasound as a random walk of phonons that are scattered by the grains. In this case, D=cl/3, where l is the mean scattering length. However, the random walk model is not totally appropriate because each time a phonon is scattered, its propagation direction after scattering remains somewhat correlated with its propagation direction before scattering. Moreover, in a polycrystalline aggregate, scattering of ultrasound occurs when the ultrasound travels from one grain having a specific acoustic impedance to another grain having another acoustic impedance. Thus the mean scattering length should be strongly related to the dimensions of the grains. In particular, if a mean grain size can be defined in a meaningful manner (such as for equiaxed grains), these dimensions may be taken as the mean grain size. Thus, more generally, one expects that D is related with l, which is itself related to the dimensions of the grains or xe2x80x9cgrain sizexe2x80x9d, d. The dimensionless quantity for grain size is kd. Therefore, one would expect that there should be a general relationship between Dk/c and kd.
Instead of assuming a specific relationship between these two quantities (such as a power law), one may simply plot one variable as a function of the other one and so obtain a xe2x80x9ccalibration curvexe2x80x9d. This calibration curve relates the measured diffusivity to grain size, taking into account the wavevector k, and the sound velocity of the material. In other words, as long as all factors affecting D other than k and c are constant, the calibration procedure is reliable. One example of applicability of this calibration curve would be to measure the grain size of a specific metallic alloy where grain size has been affected by thermal processing.
The above analysis is complicated by the fact that there is not one scattering length, but several. The scattering length is different for each ultrasonic mode: longitudinal, transverse, surface waves, plate waves, or other special modes. However, because there is local equipartition of energy, and because the various ultrasonic modes are converted into one-another, D may be considered as a mean diffusion coefficient that is formed by the average of the diffusion coefficients of all acoustic modes, weighted by the probability of occupation for each mode. Therefore, the general conclusion that there must be a general relationship between Dk/c and kd holds.
Consequently, in a further aspect the invention provides a method of determining grain size in a target sample of material, comprising the steps of building a calibration of kd vs Dk/c, based on the measurement of D at one or several values of k on several calibration samples which are similar to the target sample but which differ with respect to their grain size, where D is the diffusion coefficient, k is the wavenumber of the ultrasound, d is the grain size and c is the velocity of sound; measuring the diffusion coefficient D at one or more values of k in the target sample; and determining the grain size in the target sample from the measured diffusion coefficient using said calibration.